摘要
在详细讨论一个辛映射的过程中 ,我们注意到轨道在相空间不同区域有着不同的扩散规律 :在充分发展的混沌区 ,残余的轨道数目随时间按指数律衰减 ;在混合区域 ,则是代数律· 在相空间中特定的区域 ,扩散还可以用对数律描述· 在一个稳定的岛屿附近 ,逃逸时间的对数随着离开岛屿的距离的增大而线性下降 ;而当逼近岛屿的时候 ,逃逸时间极迅速地上升 ,与不变曲线的超指数稳定性一致· 利用此映射研究小行星运动时 ,它的不动点及其稳定性可解释小行星的分布· 此外 ,本文还讨论了在 4 :3,3:2和 2 :1共振处小行星轨道的扩散速度·
A symplectic mapping is studied carefully. The exponential diffusion law in developed chaotic region and algebraic law in mixed region were observed. An area was found where the diffusion follows a logarithmic law. It is shown in the vicinity of an island, the logarithm of the escape time decreases linearily as the initial position moves away from the island. But when approaching close to the island, the escape time goes up very quickly, consistent with the superexponential stability of the invariant curve. When applied to the motion of asteroid, this mapping's fixed points and their stabilities give an explanation of the distribution of asteroids. The diffusion velocities in 4∶3,3∶2 and 2∶1 jovian resonances are also investigated.
出处
《应用数学和力学》
EI
CSCD
北大核心
2001年第7期719-728,共10页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目 (196 330 10
1990 30 0 1)
